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(i) Draw a neat labelled diagram of a cyclotron.

(ii) Show that time period of ions in cyclotron is independent of both the speed of ion and radius of circular path. What is the significance of this property?

(iii) An electron after being accelerated through a potential difference of 100 V enters a uniform magnetic field of 0.004 perpendicular to its direction of motion. Calculate the radius of the path described by the electron.

 

 

 

 
 
 
 
 

Answers (1)

(ii)

\frac{mv^{2}}{r}=qvB

r=\frac{mv}{qB}

Time period

T = \frac{2\pi r}{v}

 =2\pi \left ( \frac{mv}{qBv} \right )

 T=\frac{2\pi m}{qB}

So the time period is independent of the speed of ion and radius of the circular path.

Significance: It helps in achieving resonance condition.

(iii) r=\frac{\sqrt{2mqV}}{qB}=\frac{\sqrt{2\times 9\times 10^{-31}\times 1.6\times 10^{-19}\times 100}}{1.6\times 10^{-19}\times 0.004}

=8.4\times 10^{-3}m

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Safeer PP

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